Problem: Rewrite as a simplified fraction. ${1.1\overline{90} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1190.909...\\ 10x &= 11.909...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1179}$ ${x = \dfrac{1179}{990}} $ ${x = \dfrac{131}{110}} \text{or} {1 \dfrac{21}{110}}$